A viable fully on-line adaptive brain computer interface (BCI) is introduced. On-line experiments with nine naive and able-bodied subjects were carried out using a continuously adaptive BCI system. The data were analyzed and the viability of the system was studied. The BCI was based on motor imagery, the feature extraction was performed with an adaptive autoregressive model and the classifier used was an adaptive quadratic discriminant analysis. The classifier was on-line updated by an adaptive estimation of the information matrix (ADIM). The system was also able to provide continuous feedback to the subject. The success of the feedback was studied analyzing the error rate and mutual information of each session and this analysis showed a clear improvement of the subject's control of the BCI from session to session.